Faster variational quantum algorithms with quantum kernel-based surrogate models

We present a new optimization strategy for small-to-intermediate scale variational quantum algorithms (VQAs) on noisy near-term quantum processors which uses a Gaussian process surrogate model equipped with a classically-evaluated quantum kernel. VQAs are typically optimized using gradient-based approaches however these are difficult to implement on current noisy devices, requiring large numbers of objective function evaluations. Our approach shifts this computational burden onto the classical optimizer component of these hybrid algorithms, greatly reducing the number of quantum circuit evaluations required from the quantum processor. We focus on the variational quantum eigensolver (VQE) algorithm and demonstrate numerically that these surrogate models are particularly well suited to the algorithm's objective function. Next, we apply these models to both noiseless and noisy VQE simulations and show that they exhibit better performance than widely-used classical kernels in terms of final accuracy and convergence speed. Compared to the typically-used stochastic gradient-descent approach to VQAs, our quantum kernel-based approach is found to consistently achieve significantly higher accuracy while requiring less than an order of magnitude fewer quantum circuit executions. We analyze the performance of the quantum kernel-based models in terms of the kernels' induced feature spaces and explicitly construct their feature maps. Finally, we describe a scheme for approximating the best-performing quantum kernel using a classically-efficient tensor network representation of its input state and so provide a pathway for scaling this strategy to larger systems

Classical and nonclassical time dilation for quantum clocks

Proper time, ideal clocks, and boosts are well understood classically, but subtleties arise in quantum physics. We show that quantum clocks set in motion via momentum boosts do not witness classical time dilation. However, using velocity boosts we find the ideal behavior in both cases, where the quantum clock and classical observer are set in motion. Without internal state-dependent forces additional effects arise. As such, we derive observed frequency shifts in ion trap atomic clocks, indicating a small additional shift, and also show the emergence of nonideal behavior in a theoretical clock model

A multi-exon deletion within WWOX is associated with a 46,XY disorder of sex development

Disorders of sex development (DSD) are congenital conditions where chromosomal, gonad or genital development is atypical. In a significant proportion of 46,XY DSD cases it is not possible to identify a causative mutation, making genetic counseling difficult and potentially hindering optimal treatment. Here, we describe the analysis of a 46,XY DSD patient that presented at birth with ambiguous genitalia. Histological analysis of the surgically removed gonads showed bilateral undifferentiated gonadal tissue and immature testis, both containing malignant germ cells. We screened genomic DNA from this patient for deletions and duplications using an Illumina whole-genome SNP microarray. This analysis revealed a heterozygous deletion within the WWOX gene on chromosome 16, removing exons 6-8. Analysis of parental DNA showed that the deletion was inherited from the mother. cDNA analysis confirmed that the deletion maintained the reading frame, with exon 5 being spliced directly onto exon 9. This deletion is the first description of a germline rearrangement affecting the coding sequence of WWOX in humans. Previously described Wwox knockout mouse models showed gonadal abnormalities, supporting a role for WWOX in human gonad development

Quantum delocalized interactions

Classical mechanics obeys the intuitive logic that a physical event happens at a definite spatial point. Entanglement, however, breaks this logic by enabling interactions without a specific location. In this work we study these delocalized interactions. These are quantum interactions that create less locational information than would be possible classically, as captured by the disturbance induced on some spatial superposition state. We introduce quantum games to capture the effect and demonstrate a direct operational use for quantum concurrence in that it bounds the nonclassical performance gain. We also find a connection with quantum teleportation, and demonstrate the games using an IBM quantum processor

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Rac1 and Rac3 isoform activation is involved in the invasive and metastatic phenotype of human breast cancer cells

INTRODUCTION: The metastatic progression of cancer is a direct result of the disregulation of numerous cellular signaling pathways, including those associated with adhesion, migration, and invasion. Members of the Rac family of small GTPases are known to act as regulators of actin cytoskeletal structures and strongly influence the cellular processes of integrin-mediated adhesion and migration. Even though hyperactivated Rac proteins have been shown to influence metastatic processes, these proteins have never been directly linked to metastatic progression. METHODS: To investigate a role for Rac and Cdc42 in metastatic breast cancer cell invasion and migration, relative endogenous Rac or Cdc42 activity was determined in a panel of metastatic variants of the MDA-MB-435 metastatic human breast cancer cell line using a p21-binding domain-PAK pull down assay. To investigate the migratory and invasive potential of the Rac isoforms in human breast cancer, namely Rac1 and the subsequently cloned Rac3, we stably expressed either dominant active Rac1 or dominant active Rac3 into the least metastatic cell variant. Dominant negative Rac1 or dominant negative Rac3 were stably expressed in the most metastatic cell variant. Cell lines expressing mutant Rac1 or Rac3 were analyzed using in vitro adhesion, migration and invasion assays. RESULTS: We show that increased activation of Rac proteins directly correlates with increasing metastatic potential in a panel of cell variants derived from a single metastatic breast cancer cell line (MDA-MB-435). The same correlation could not be found with activated Cdc42. Expression of a dominant active Rac1 or a dominant active Rac3 resulted in a more invasive and motile phenotype. Moreover, expression of either dominant negative Rac1 or dominant negative Rac3 into the most metastatic cell variant resulted in decreased invasive and motile properties. CONCLUSION: This study correlates endogenous Rac activity with high metastatic potential and implicates Rac in the regulation of cell migration and invasion in metastatic breast cancer cells. Taken together, these results suggest a role for both the Rac1 and Rac3 GTPases in human breast cancer progression

The Main Belt Comets and ice in the Solar System

We review the evidence for buried ice in the asteroid belt; specifically the questions around the so-called Main Belt Comets (MBCs). We summarise the evidence for water throughout the Solar System, and describe the various methods for detecting it, including remote sensing from ultraviolet to radio wavelengths. We review progress in the first decade of study of MBCs, including observations, modelling of ice survival, and discussion on their origins. We then look at which methods will likely be most effective for further progress, including the key challenge of direct detection of (escaping) water in these bodies

Impact of exposure measurement error in air pollution epidemiology: effect of error type in time-series studies

<p>Abstract</p> <p>Background</p> <p>Two distinctly different types of measurement error are Berkson and classical. Impacts of measurement error in epidemiologic studies of ambient air pollution are expected to depend on error type. We characterize measurement error due to instrument imprecision and spatial variability as multiplicative (i.e. additive on the log scale) and model it over a range of error types to assess impacts on risk ratio estimates both on a per measurement unit basis and on a per interquartile range (IQR) basis in a time-series study in Atlanta.</p> <p>Methods</p> <p>Daily measures of twelve ambient air pollutants were analyzed: NO₂, NO_x, O₃, SO₂, CO, PM₁₀mass, PM_2.5mass, and PM_2.5components sulfate, nitrate, ammonium, elemental carbon and organic carbon. Semivariogram analysis was applied to assess spatial variability. Error due to this spatial variability was added to a reference pollutant time-series on the log scale using Monte Carlo simulations. Each of these time-series was exponentiated and introduced to a Poisson generalized linear model of cardiovascular disease emergency department visits.</p> <p>Results</p> <p>Measurement error resulted in reduced statistical significance for the risk ratio estimates for all amounts (corresponding to different pollutants) and types of error. When modelled as classical-type error, risk ratios were attenuated, particularly for primary air pollutants, with average attenuation in risk ratios on a per unit of measurement basis ranging from 18% to 92% and on an IQR basis ranging from 18% to 86%. When modelled as Berkson-type error, risk ratios per unit of measurement were biased away from the null hypothesis by 2% to 31%, whereas risk ratios per IQR were attenuated (i.e. biased toward the null) by 5% to 34%. For CO modelled error amount, a range of error types were simulated and effects on risk ratio bias and significance were observed.</p> <p>Conclusions</p> <p>For multiplicative error, both the amount and type of measurement error impact health effect estimates in air pollution epidemiology. By modelling instrument imprecision and spatial variability as different error types, we estimate direction and magnitude of the effects of error over a range of error types.</p

Matching Schur complement approximations for certain saddle-point systems

The solution of many practical problems described by mathematical models requires approximation methods that give rise to linear(ized) systems of equations, solving which will determine the desired approximation. This short contribution describes a particularly effective solution approach for a certain class of so-called saddle-point linear systems which arises in different contexts